function [thrustRow, thrustCol] = nautilus(chart, aIndex, bIndex, maxThrottle)
iW = chart(:,:,1);
jW = chart(:,:,2);
mt = ceil(maxThrottle/2);
mt2 = ceil(3*maxThrottle/4);
[nrow,ncol] = size(iW);
[ai,aj] = ind2sub([nrow,ncol],aIndex);
[bi,bj] = ind2sub([nrow,ncol],bIndex);
thrustRow = zeros(1,1000);
thrustCol = zeros(1,1000);
vws = inf(1,1000);
% set up initial conditions
pi = ai;
pj = aj;
vi = 0;
vj = 0;
n = 0;
mtt = 400;
% try to approach b
sqd = inf;
while (sqd>100)
sqd = inf;
mcum = 0;
stopn = 0;
srec = [pi pj vi vj];
while ((n<1000)&&((pi>=1)&(pj>=1)&(pi<=nrow)&(pj<=ncol))&&((pi~=bi)|(pj~=bj)))
[gs,ti,tj,ui,uj] = score_glide2(bi,bj,pi,pj,vi,vj,iW,jW,1000-n,mt);
[mgs,mgsi] = min(gs);
if (mgs > 1)
if (n>0)&(sqd>mtt)
% use maxThrottle to get out of difficult situation
[wk,mi,mj,ws] = pickNext2(ti,tj,ui,uj,bi,bj,iW,jW,maxThrottle,1000-n);
if (isinf(ws(wk)))
break;
end;
else
[wk,mi,mj,ws] = pickNext2(ti,tj,ui,uj,bi,bj,iW,jW,mt,1000-n);
if (isinf(ws(wk))&(mt~=maxThrottle))
[wk,mi,mj,ws] = pickNext2(ti,tj,ui,uj,bi,bj,iW,jW,mt2,1000-n);
if (isinf(ws(wk))&(mt~=maxThrottle))
[wk,mi,mj,ws] = pickNext2(ti,tj,ui,uj,bi,bj,iW,jW,maxThrottle,1000-n);
if (isinf(ws(wk)))
break;
end;
end;
end;
end;
else
ws = inf;
wk = 1;
mi = 0;
mj = 0;
end;
if (mgs<100)&(mgs <= ws(wk)+abs(mi)+abs(mj))
% end early
n = n+mgsi-1;
pi = ti(mgsi);
pj = tj(mgsi);
vi = ui(mgsi);
vj = uj(mgsi);
vws(n) = mgs;
break
end;
% stop if too much motor
mcum = mcum+abs(mi)+abs(mj);
if (mcum>sqd)
% undo moves:
thrustRow(stopn+1:n) = 0;
thrustCol(stopn+1:n) = 0;
n = stopn;
% return to position:
pi = srec(1);
pj = srec(2);
vi = srec(3);
vj = srec(4);
pi = pi+vi;
pj = pj+vj;
% add coasting
[gs,ti,tj,ui,uj] = score_glide2(bi,bj,pi,pj,vi,vj,iW,jW,1000-n,mt);
[~,mgsi] = min(gs);
n = n+mgsi-1;
pi = ti(mgsi);
pj = tj(mgsi);
vi = ui(mgsi);
vj = uj(mgsi);
break;
end;
% apply winning move
thrustRow(n+wk) = mi;
thrustCol(n+wk) = mj;
n = n+wk;
pi = ti(wk);
pj = tj(wk);
vi = ui(wk+1)+mi;
vj = uj(wk+1)+mj;
vws(n) = ws(wk);%+(pi-ai).^2+(pj-aj).^2;
if (ws(wk)<sqd)
sqd = ws(wk);
mcum = 0;
stopn = n;
srec = [pi pj vi vj];
end;
% advance one turn
pi = pi+vi;
pj = pj+vj;
end;
if (sqd > 100)
if (mt < mt2)
% reset and try again with full thrust
thrustRow = zeros(1,1000);
thrustCol = zeros(1,1000);
vws = inf(1,1000);
pi = ai;
pj = aj;
vi = 0;
vj = 0;
n = 0;
mt = mt2;
elseif (mt < maxThrottle)
% reset and try again with full thrust
thrustRow = zeros(1,1000);
thrustCol = zeros(1,1000);
vws = inf(1,1000);
pi = ai;
pj = aj;
vi = 0;
vj = 0;
n = 0;
mt = maxThrottle;
else
% give up
sqd = 0;
end;
end;
end;
bs = ws(wk);
bn = n;
mt = ceil(2*maxThrottle/3);
[vpi,vpj] = mapMoves(ai,aj,iW,jW,thrustRow(1:n),thrustCol(1:n));
dB = (vpi-bi).^2+(vpj-bj).^2;
% now try to approach a
sqd = inf;
while (bn>1)&&(sqd > dB(bn-1))
sqd = inf;
mcum = 0;
stopn = bn;
srec = [pi pj vi vj];
while ((n<1000)&&((pi>=1)&(pj>=1)&(pi<=nrow)&(pj<=ncol))&&((pi~=ai)|(pj~=aj)))
[gs,ti,tj,ui,uj] = score_glide(ai,aj,pi,pj,vi,vj,iW,jW,1000-n);
[mgs,mgsi] = min(gs);
if (mgs > 1)
if (n>bn)&(sqd>mtt)
% use maxThrottle to get out of difficult situation
[wk,mi,mj,ws] = pickNext(ti,tj,ui,uj,ai,aj,iW,jW,maxThrottle,1000-n);
if (isinf(ws(wk)))
break;
end;
else
[wk,mi,mj,ws] = pickNext(ti,tj,ui,uj,ai,aj,iW,jW,mt,1000-n);
if (isinf(ws(wk)))
[wk,mi,mj,ws] = pickNext(ti,tj,ui,uj,ai,aj,iW,jW,mt2,1000-n);
if (isinf(ws(wk)))
[wk,mi,mj,ws] = pickNext(ti,tj,ui,uj,ai,aj,iW,jW,maxThrottle,1000-n);
if (isinf(ws(wk)))
break;
end;
end;
end;
end;
else
ws = inf;
wk = 1;
mi = 0;
mj = 0;
end;
if (mgs<100)&(mgs <= ws(wk)+abs(mi)+abs(mj))
% end early
n = n+mgsi-1;
pi = ti(mgsi);
pj = tj(mgsi);
vi = ui(mgsi);
vj = uj(mgsi);
vws(n) = mgs;
break
end;
% stop if too much motor
mcum = mcum+abs(mi)+abs(mj);
if (isinf(ws(wk)))|(mcum>sqd)
% undo moves:
thrustRow(stopn+1:n) = 0;
thrustCol(stopn+1:n) = 0;
n = stopn;
% return to position:
pi = srec(1);
pj = srec(2);
vi = srec(3);
vj = srec(4);
pi = pi+vi;
pj = pj+vj;
% add coasting
[gs,ti,tj,ui,uj] = score_glide2(bi,bj,pi,pj,vi,vj,iW,jW,1000-n,mt);
[~,mgsi] = min(gs);
n = n+mgsi-1;
pi = ti(mgsi);
pj = tj(mgsi);
vi = ui(mgsi);
vj = uj(mgsi);
break;
end;
% apply winning move
thrustRow(n+wk) = mi;
thrustCol(n+wk) = mj;
n = n+wk;
pi = ti(wk);
pj = tj(wk);
vi = ui(wk+1)+mi;
vj = uj(wk+1)+mj;
vws(n) = bs+ws(wk);
if (ws(wk)<sqd)
sqd = ws(wk);
mcum = 0;
stopn = n;
srec = [pi pj vi vj];
end;
% advance one turn
pi = pi+vi;
pj = pj+vj;
end;
if (bn>1)&&(sqd > dB(bn-1))
% prepare for repeat
thrustRow(bn:n) = 0;
thrustCol(bn:n) = 0;
bn = bn-1;
n = bn;
pi = ai;
pj = aj;
vi = 0;
vj = 0;
for k = 1:n
vi = vi+iW(pi,pj)+thrustRow(k);
vj = vj+jW(pi,pj)+thrustCol(k);
pi = pi+vi;
pj = pj+vj;
end;
sqd = inf;
end;
end;
% trim excess
thrustRow = thrustRow(1:n);
thrustCol = thrustCol(1:n);
end
function [wk,mi,mj,ws] = pickNext(ti,tj,ui,uj,gi,gj,iW,jW,mt,N)
n = numel(ti);
wvi = zeros(1,n);
wvj = zeros(1,n);
ws = zeros(1,n);
for k = 1:n
ks = inf(2*mt+1);
for i = -mt:mt
for j = -(mt-abs(i)):(mt-abs(i))
ks(i+mt+1,j+mt+1) = min(score_glide(gi,gj,ti(k),tj(k),ui(k)+i,uj(k)+j,iW,jW,N-k))+abs(i)+abs(j);
end;
end;
ks(mt+1,mt+1) = inf;
[m1,m1i] = min(ks);
[ws(k),m2i] = min(m1);
wvi(k) = m1i(m2i)-mt-1;
wvj(k) = m2i-mt-1;
ws(k) = ws(k)-abs(wvi(k))-abs(wvj(k));
end;
[~,wk] = min(ws);
mi = wvi(wk);
mj = wvj(wk);
end
function [wk,mi,mj,ws] = pickNext2(ti,tj,ui,uj,gi,gj,iW,jW,mt,N)
[nrow,ncol] = size(iW);
n = numel(ti);
wvi = zeros(1,n);
wvj = zeros(1,n);
ws = zeros(1,n);
for k = 1:n
ks = inf(2*mt+1);
for i = -mt:mt
for j = -(mt-abs(i)):(mt-abs(i))
ks(i+mt+1,j+mt+1) = min(score_glide2(gi,gj,ti(k),tj(k),ui(k)+i,uj(k)+j,iW,jW,N-k,mt))+abs(i)+abs(j);
end;
end;
ks(mt+1,mt+1) = inf;
[m1,m1i] = min(ks);
[ws(k),m2i] = min(m1);
wvi(k) = m1i(m2i)-mt-1;
wvj(k) = m2i-mt-1;
ws(k) = ws(k)-abs(wvi(k))-abs(wvj(k));
end;
[mws,wk] = min(ws);
if isinf(mws)
mi = 0;
mj = 0;
else
mi = wvi(wk);
mj = wvj(wk);
end;
end
function [s,ti,tj,ui,uj] = score_glide(gi,gj,pi,pj,vi,vj,iW,jW,n)
[ti,tj,ui,uj] = glide(pi,pj,vi,vj,iW,jW,n);
s = (ti-gi).^2+(tj-gj).^2;
s(1) = inf;
end
function [s,ti,tj,ui,uj] = score_glide2(gi,gj,pi,pj,vi,vj,iW,jW,n,mt)
[ti,tj,ui,uj] = glide(pi,pj,vi,vj,iW,jW,n);
s = (ti-gi).^2+(tj-gj).^2+max(0,abs(ui(2:end))+abs(uj(2:end))-mt/3).^2;
s(1) = inf;
end
% returns the future trajectory given initial point and velocity
% computes up to n steps ahead
function [ti,tj,ui,uj] = glide(pi,pj,vi,vj,iW,jW,n)
[nrow,ncol] = size(iW);
%seen = cell(nrow,ncol);
seen = false(nrow,ncol);
ti = zeros(1,n);
tj = zeros(1,n);
ui = zeros(1,n);
uj = zeros(1,n);
ti(1) = pi;
tj(1) = pj;
ui(1) = vi;
uj(1) = vj;
ui(2) = vi+iW(pi,pj);
uj(2) = vj+jW(pi,pj);
for k = 2:n
%seen{pi,pj} = [seen{pi,pj}; vi,vj];
seen(pi,pj) = true;
vi = ui(k);
vj = uj(k);
pi = pi+vi;
pj = pj+vj;
if (((pi<1)|(pj<1)|(pi>nrow)|(pj>ncol))||(seen(pi,pj)))
ti = ti(1:k-1);
tj = tj(1:k-1);
ui = ui(1:k);
uj = uj(1:k);
break;
end;
ti(k) = pi;
tj(k) = pj;
ui(k+1) = vi+iW(pi,pj);
uj(k+1) = vj+jW(pi,pj);
end;
end
function [vpi,vpj,vvi,vvj] = mapMoves(ai,aj,iW,jW,thrustRow,thrustCol)
n = numel(thrustRow);
vpi = zeros(1,n+1);
vpj = zeros(1,n+1);
vvi = zeros(1,n+1);
vvj = zeros(1,n+1);
vpi(1) = ai;
vpj(1) = aj;
vvi(1) = 0;
vvj(1) = 0;
for k = 1:n
vvi(k+1) = vvi(k)+iW(vpi(k),vpj(k))+thrustRow(k);
vvj(k+1) = vvj(k)+jW(vpi(k),vpj(k))+thrustCol(k);
vpi(k+1) = vpi(k)+vvi(k+1);
vpj(k+1) = vpj(k)+vvj(k+1);
end;
end
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